US11520857B2 - Storage medium and data processing method - Google Patents
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- US11520857B2 US11520857B2 US16/801,652 US202016801652A US11520857B2 US 11520857 B2 US11520857 B2 US 11520857B2 US 202016801652 A US202016801652 A US 202016801652A US 11520857 B2 US11520857 B2 US 11520857B2
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
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- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/02—Neural networks
- G06N3/08—Learning methods
- G06N3/088—Non-supervised learning, e.g. competitive learning
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T9/00—Image coding
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/06—Power analysis or power optimisation
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N20/00—Machine learning
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/02—Neural networks
- G06N3/04—Architecture, e.g. interconnection topology
- G06N3/045—Combinations of networks
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- G06—COMPUTING; CALCULATING OR COUNTING
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- G06N3/00—Computing arrangements based on biological models
- G06N3/02—Neural networks
- G06N3/04—Architecture, e.g. interconnection topology
- G06N3/047—Probabilistic or stochastic networks
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- G06N3/0472—
Definitions
- the embodiments discussed herein relate to a storage medium and a data processing method.
- a design space is set by combining design variables indicating circuit parameters.
- the design variables are used to describe an objective function so that an optimization problem is formulated.
- searching processing is performed which searches an optimum solution (global solution) for optimizing the objective function.
- the solution space that is a curved surface of the objective function in the design space is multimodal.
- a plurality of mountains and valleys may exist in the solution space.
- the searching result is easily trapped in a local solution instead of a global solution.
- metaheuristics include simulated annealing, genetic algorithm and so on.
- a circuit parameter design method has been known which considers not only variations of performances of manufactured product circuits but also minimization of losses due to the variations (see Japanese Laid-open Patent Publication No. 2000-293556, for example).
- An information processing apparatus has also been known which executes machine learning with a combination of a recursive neural network and a variational autoencoder.
- Japanese Laid-open Patent Publication No. 2000-293556 and Japanese Laid-open Patent Publication No. 2018-152004 have been disclosed.
- a non-transitory computer-readable storage medium storing a program that causes a computer to execute a process, the process includes acquiring, based on a compression model that is acquired by learning processing on a set of data generated by using a combination of values of variables and that compresses dimensions of data, a point corresponding to data generated by using a predetermined combination of the values of variables within a compressed space; acquiring, based on the point corresponding to the data generated by using the predetermined combination, a target point within the space corresponding to a target value of a characteristic changing in accordance with the values of variables, and a regression model within the space for a predetermined variable of variables, a change amount of the predetermined variable; and changing the value of the predetermined variable included in the predetermined combination by using the change amount.
- FIG. 1 is a functional configuration diagram of a data processing apparatus
- FIG. 2 is a flowchart of data processing
- FIG. 3 is a functional configuration diagram of a specific example of the data processing apparatus
- FIG. 4 is a diagram illustrating a VAE in a circuit design of, a power supply circuit
- FIG. 5 is a diagram illustrating images plotted in a latent space
- FIG. 6 is a diagram illustrating learning processing on a VAE
- FIGS. 7 A and 7 B are diagrams illustrating a ramp function and a sigmoid function
- FIG. 8 is a flowchart of learning processing
- FIG. 9 is a flowchart of searching processing
- FIG. 10 is a diagram illustrating a power supply circuit
- FIG. 11 is a diagram illustrating images of voltage waveforms
- FIG. 12 is a diagram illustrating coefficients of determination against circuit parameters.
- FIG. 13 is a configuration diagram of an information processing apparatus.
- a common characteristic among conventional methods such as mathematical programming, metaheuristics and response surface methodology is that the iteration count for finding a global solution is reduced by devising the searching processing in the design space.
- the objective function is described by using design variables, the structure of the solution space is maintained, and a plurality of mountains and valleys still exist in the solution space. Because of that, the time for searching a global solution may not be reduced.
- FIG. 1 illustrates a functional configuration example of a data processing apparatus according to an embodiment.
- a data processing apparatus 101 in FIG. 1 includes a storage unit 111 and a changing unit 112 .
- the storage unit 111 stores a compression model 121 that is acquired by learning processing performed on a set of data generated by using a combination of values of a plurality of variables and that compresses the dimensions of the data.
- the changing unit 112 performs data processing by using the compression model 121 .
- FIG. 2 is a flowchart illustrating an example of data processing performed by the data processing apparatus 101 in FIG. 1 .
- the changing unit 112 acquires a point corresponding to the data generated by using a predetermined combination of values of a plurality of variables within a compressed space based on the compression model 121 (step 201 ).
- the changing unit 112 acquires a change amount of a predetermined variable among the plurality of variables (step 202 ).
- the target point within the compressed space is a point corresponding to a target value of a characteristic that varies in accordance with the values of the plurality of variables
- the regression model within the compressed space is a regression model for the predetermined variable.
- the changing unit 112 changes the value of the predetermined variable included in the predetermined combination by using the acquired change amount (step 203 ).
- FIG. 3 illustrates a specific example of the data processing apparatus 101 in FIG. 1 .
- a data processing apparatus 301 in FIG. 3 includes a storage unit 311 , a simulator 312 , an image generating unit 313 , a learning unit 314 , a regression analysis unit 315 , a searching unit 316 and an output unit 317 .
- the storage unit 311 and the searching unit 316 correspond to the storage unit 111 and the changing unit 112 in FIG. 1 , respectively.
- the data processing apparatus 301 performs data processing for optimizing parameters of an analysis target by using artificial intelligence.
- the analysis target in circuit design is an electric circuit, an electronic circuit or the like
- the parameters in circuit design are a resistance value, a capacitance, an inductance and the like.
- the data processing apparatus 301 may also perform data processing such as structural analysis, electromagnetic field analysis, fluid analysis, and image analysis.
- the analysis target in structural analysis is a building, a product or the like and the analysis target in electromagnetic field analysis is a wireless communication circuit, an antenna or the like.
- the analysis target in fluid analysis is air, water or the like, and the analysis target in image analysis is an image of any one of various objects.
- the storage unit 311 stores a parameter set 321 and initial parameters 329 .
- the parameter set 321 and the initial parameters 329 include values of variables representing a plurality of parameters of an analysis target.
- the parameter set 321 is a set of a plurality of combinations of values of a plurality of variables to be used for learning processing.
- the initial parameters 329 include a combination of values of a plurality of variables indicating initial values for searching processing.
- the simulator 312 executes a simulation on an analysis target by using the parameter set 321 to generate a set of time-series data representing a simulation result and store it in the storage unit 311 as time-series data set 322 .
- the simulator 312 generates a set of characteristic values of the analysis target corresponding to a plurality of time-series data pieces and store it in the storage unit 311 as a characteristic value set 323 .
- a characteristic of an analysis target varies in accordance with values of a plurality of parameters, and a simulation using combinations included in the parameter set 321 determines characteristic values corresponding to the combinations. For example, as a characteristic in circuit design of a power supply circuit, the efficiency of the power supply circuit may be used.
- the image generating unit 313 generates images representing time-series data pieces included in the time-series data set 322 and stores a set of images generated from the plurality of time-series data pieces in the storage unit 311 as an image set 324 .
- the image set 324 corresponds to a set of data pieces to be learned.
- the learning unit 314 performs learning processing on the image set 324 to generate a variational autoencoder (VAE) 325 and stores it in the storage unit 311 .
- VAE variational autoencoder
- the VAE 325 corresponds to the compression model 121 in FIG. 1 .
- An autoencoder is a compression model that generates a latent space representation being a characteristic representation having a reduced amount of information because of compression of the dimensions of input data by using a neural network.
- the latent space represents a low-dimensional space after a compression.
- the VAE is a compression model applying a probability distribution to latent variables representing the latent space of the AE.
- FIG. 4 illustrates an example of the VAE 325 in circuit design of a power supply circuit.
- the VAE 325 in FIG. 4 includes encoders 401 and decoders 402 and generates an output image 412 from an input image 411 .
- the input image 411 represents a time-series data of voltage (voltage waveform) at a node within the power supply circuit, which is generated by a circuit simulation on the power supply circuit.
- the value of a latent variable z is calculated based on a probability distribution having an average ⁇ and a distribution ⁇ .
- the encoders 401 convert the input image 411 to ⁇ and ⁇ , and the decoders 402 convert z calculated based on the ⁇ and ⁇ to the output image 412 .
- the learning unit 314 learns the parameters of the encoders 401 and the decoders 402 by using the images of the voltage waveforms generated by the circuit simulation using the parameter set 321 as the input image 411 for training.
- the regression analysis unit 315 generates a regression model 326 for the variables representing the parameters of the analysis target by using the image set 324 and the VAE 325 and stores it in the storage unit 311 .
- An objective variable of the regression model 326 is a variable representing a parameter of an analysis target
- explanatory variables of the regression model 326 are a plurality of latent variables representing a latent space of the VAE 325 .
- the regression analysis unit 315 acquires a coefficient of determination 327 for the regression model 326 by using the image set 324 , the VAE 325 , and the regression model 326 and stores it in the storage unit 311 .
- the coefficient of determination 327 is an example of a reliability representing the reliability of the regression model 326 , and the reliability of the regression model 326 increases as the coefficient of determination 327 increases.
- the regression analysis unit 315 acquires a target average value 328 of each latent variable corresponding to a target value of a characteristic and stores it in the storage unit 311 .
- the target average value 328 of each of a plurality of latent variables represents a target point within the latent space.
- the regression model 326 , the coefficient of determination 327 and the target average value 328 along with the VAE 325 are acquired in the learning processing so that efficient searching processing is implemented based on the information.
- the simulator 312 In the searching processing, the simulator 312 generates time-series data by executing a simulation using the initial parameters 329 and calculates a characteristic value for the time-series data.
- the image generating unit 313 generates an image representing the generated time-series data.
- the searching unit 316 acquires an initial average value of each of the latent variables by using the VAE 325 from the image generated by using the initial parameters 329 .
- An initial average value of each of the plurality of latent variables represents a search starting point within the latent space.
- the searching unit 316 acquires a change amount of each of the variables from the initial average values and the target average values 328 by using the regression model 326 for the variables and changes the values of the variables included in the initial parameters 329 by using the change amounts.
- the searching unit 316 uses the regression model 326 to acquire a first value of each of the variables from the target average value 328 and acquire a second value of each of the variables from the initial average value and acquires a change amount by using a difference between the first value and the second value and the coefficient of determination 327 .
- the change amount reflects a difference between the search starting point and the target point within the latent space and the reliability of the regression model 326 .
- the simulator 312 generates time-series data by executing a simulation using the changed values of the variables and calculates characteristic value for the time-series data.
- the image generating unit 313 If the difference between the calculated characteristic value and the target value is higher than a threshold value, the image generating unit 313 generates an image representing the generated time-series data. Next, the searching unit 316 acquires an average value of each of the latent variables from the generated image by using the VAE 325 . An average value of each of the plurality of latent variables represents a current search point within the latent space.
- the searching unit 316 acquires a change amount of each of the variables from the average values representing the current search points and the target average values 328 by using the regression model 326 for the variables and further changes the values of the changed variables by using the change amounts.
- the searching unit 316 acquires change amounts from the changed values by using the average values representing the current search points instead of the initial average values in the same manner as the processing for the change amounts from the initial parameters 329 .
- the change amount reflects a difference between the current search points and the target point within the latent space and the reliability of the regression model 326 .
- the simulator 312 , the image generating unit 313 and the searching unit 316 repeat the processing of changing the values of the variables until the difference between the characteristic value and the target value gets lower than the threshold value.
- the searching unit 316 stores the values of the variables in the storage unit 311 as proper parameters 330 , and the output unit 317 outputs the proper parameters 330 .
- the data processing apparatus 301 generates a circuit diagram of an electric circuit or an electronic circuit by using circuit parameters represented by the proper parameters 330 .
- the data processing apparatus 301 generates a design drawing for a building, a product or the like by using the proper parameters 330 .
- the data processing apparatus 301 In a case where the data processing is an electromagnetic field analysis, the data processing apparatus 301 generates a design drawing for a wireless communication circuit, an antenna or the like by using the proper parameters 330 . In a case where the data processing is a fluid analysis, the data processing apparatus 301 generates an analysis result with respect to a flow of air, water or the like by using the proper parameters 330 . In a case where the data processing is an image analysis, the data processing apparatus 301 generates an analysis result with respect to an image of an object by using the proper parameters 330 .
- FIG. 5 illustrates an example of images plotted in the latent space of the VAE 325 in FIG. 4 .
- the latent space in FIG. 5 is a two-dimensional plane, and two latent variables represent two-dimensional coordinates on the plane.
- images illustrating voltage waveforms at nodes within a power supply circuit are plotted at positions indicated by the values of the latent variables generated by the VAE 325 .
- the circuit parameters for generating the voltage waveforms are also similar. Therefore, it may be considered that the circuit parameters for a plurality of voltage waveforms aligned in a specific direction within the latent space change serially in the direction.
- the circuit parameters may be rapidly and easily optimized.
- ⁇ j represents the jth element of the time-series data set ⁇
- o represents the number of focus points of the analysis target.
- the focus points correspond to nodes within a circuit.
- the focus points correspond to nodes of a computational grid.
- ⁇ j represents the jth element (characteristic value) of the characteristic set ⁇ .
- Xj represents the jth element of the image set ⁇
- images G1 to Go may collectively be called “image Xj”.
- FIG. 6 illustrates learning processing on the VAE 325 .
- the VAE 325 in FIG. 6 includes an encoder 601 and a decoder 602 and generates an output image X′ from an input image X.
- the input image X corresponds to the image Xj in Expression (8).
- the encoder 601 has a probability distribution Q
- the decoder 602 has a probability distribution R.
- the encoder 601 and the decoder 602 are generated by using a hierarchical neural network and include weights and biases as parameters.
- a latent variable Z is equivalent to an n-dimensional vector randomly sampled from n-dimensional normal distribution N( ⁇ , ⁇ ) of an average ⁇ and a distribution ⁇ and is expressed by the following expression.
- ⁇ represents an n-dimensional vector randomly sampled from an n-dimensional standard normal distribution N(0, I), and is a product (Hadamard product) of each element of two vectors.
- the encoder 601 converts the input image X to ⁇ and ⁇ and the decoder 602 converts the latent variable Z calculated by Expression (10) by using the ⁇ and ⁇ to the output image X′.
- the input image X has o ⁇ u dimensions
- the latent variable Z has n dimensions.
- the first term of the right side of Expression (11) represents a regularized loss
- the second term represents a reconstruction loss
- D KL (PA ⁇ PB) is a scale for measuring a difference between a probability distribution PA and a probability distribution PB and is called “Kullback-Leibler divergence”.
- the Kullback-Leibler divergence is equal to zero only when PA and PB are completely matched and otherwise it is equal to a positive value.
- E[A] represents an expected value of A.
- a square sum error, a cross entropy error or the like between the input image X and the output image X′ is used.
- the learning unit 314 learns parameters of the encoder 601 and the decoder 602 for the image set ⁇ in Expression (7) such that the loss L in Expression (11) is minimized. Minimization of the regularized loss allows conversion of images that are similar to each other to points that are close to each other within the latent space.
- the regression analysis unit 315 performs a regression analysis on each variable pi to generate the regression model 326 .
- the regression analysis unit 315 inputs the image set ⁇ to the encoder 601 and generates a set M of the average values of the latent variable Z.
- ⁇ j ( ⁇ j (1), ⁇ j (2), . . . , ⁇ j ( n )) (13)
- the regression analysis unit 315 generates a normal equation as follows for each variable p(i).
- ⁇ i and ⁇ i(d) are parameters of a multiple linear regression model.
- the regression analysis unit 315 solves the normal equation by the least squares method to acquire of and ⁇ i(d).
- the regression hyperplane of Expression (15) represents the regression model 326 for the variable p(i).
- the regression analysis unit 315 acquires a coefficient of determination 327 for the regression model 326 by using the image set ⁇ of Expression (7), the VAE 325 , and the regression hyperplane of Expression (15).
- yj ( i ) ⁇ i+ ⁇ i (1) ⁇ j (1)+ ⁇ i (2) ⁇ j (2)+ . . . + ⁇ i ( n ) ⁇ j ( n ) (16)
- the regression analysis unit 315 calculates a coefficient of determination Ri 2 of the regression model 326 for the variable p(i).
- p AVE (i) represents an average value of p1(i) to pk(i).
- Ri 2 increases as the number of explanatory variables increases. Therefore, in order to compare values of Ri 2 by changing the dimension of the latent space, an operation such as using Ri 2 having an adjusted degree of freedom is preferably performed.
- the regression analysis unit 315 associates the characteristic values ⁇ j included in the characteristic value set ⁇ of Expression (6) and the average values ⁇ j included in the set M of the average values, selects the average value ⁇ j corresponding to the target value ⁇ t of the characteristic of the analysis target, and records it as a target average value ⁇ t.
- the simulator 312 In the searching processing, the simulator 312 generates time-series data by executing a simulation using the current values of p( 1 ) to p(m) and calculates a characteristic value ⁇ c for the time-series data.
- the image generating unit 313 generates an image Xc representing the generated time-series data.
- the searching unit 316 inputs the image Xc to the encoder 601 and generates an average value pc of the latent variable Z.
- the searching unit 316 calculates an estimated value yi( ⁇ t) of p(i) from the average value ⁇ t and calculates an estimated value yi( ⁇ c) of p(i) from the average value ⁇ c.
- the searching unit 316 calculates a change amount ⁇ p(i) by the following expressions.
- ⁇ p ( i ) F ( Ri 2 ) ⁇ yi (21)
- ⁇ yi yi ( ⁇ t ) ⁇ yi ( ⁇ c ) (22)
- F(Ri 2 ) represents a monotonically increasing function of the coefficient of determination Ri 2 .
- ⁇ yi is multiplied by F(Ri 2 ) to reflect the likelihood of the multiple linear regression to ⁇ p(i).
- the searching unit 316 updates the current values of p( 1 ) to p(m) by the following Expression.
- p ( i ) p ( i )+ ⁇ p ( i ) (23)
- the parameters of the analysis target may be brought closer to the value that realizes the target value ⁇ t.
- the simulator 312 generates time-series data by executing a simulation using the values of the updated p(i) and calculates a characteristic value ⁇ c for the time-series data.
- the image generating unit 313 generates an image Xc representing the generated time-series data.
- the characteristic value ⁇ c and the image Xc are updated.
- the searching unit 316 repeats the update of p(i) until the difference between the updated characteristic value ⁇ c and the target value ⁇ t gets lower than a threshold value.
- g in Expression (24) and Expression (25) represents a gain, and ⁇ represents a threshold value. Because the reliability of the regression model 326 decreases as the coefficient of determination Ri 2 decreases, it is desirably not to update the value of p(i) when the coefficient of determination Ri 2 is lower than a predetermined value. Accordingly, in Expression (24) and Expression (25), the value of the function F(x) is set to 0 when x is lower than the threshold value ⁇ . Other functions having a characteristic similar to a sigmoid function may be used as the function F(x).
- FIGS. 7 A and 7 B illustrate a ramp function and a sigmoid function for a plurality of values of the gain g.
- FIG. 7 B illustrates an example of a sigmoid function of Expression (25).
- ⁇ 0.3
- setting a large value as the gain g may rapidly bring the value of p(i) closer to the direction of the optimum value.
- setting a small value as the gain g ay gradually bring the value of p(i) closer to the direction of the optimum value.
- FIG. 8 is a flowchart illustrating an example of the learning processing performed by the data processing apparatus 301 in FIG. 3 .
- the simulator 312 generates a parameter set 321 (step 801 ) and executes a simulation by using the parameter set 321 so that a time-series data set 322 and a characteristic value set 323 are generated (step 802 ).
- the image generating unit 313 generates an image set 324 from the time-series data set 322 (step 803 ), and the learning unit 314 performs learning processing on the image set 324 to generate a VAE 325 (step 804 ).
- the regression analysis unit 315 inputs the image set 324 to the VAE 325 and generates a set of the average values of the latent variable Z (step 805 ).
- the regression analysis unit 315 generates a normal equation for each variable p(i) by using the set of the average values and solves the normal equations to acquire an equation of a regression hyperplane within the latent space so that a regression model 326 is generated (step 806 ).
- the regression analysis unit 315 acquires a coefficient of determination 327 for the regression model 326 by using the image set 324 , the VAE 325 , and the regression model 326 (step 807 ).
- the regression analysis unit 315 associates the characteristic values included in the characteristic value set 323 and average values included in the set of the average values of the latent variables Z (step 808 ) and acquires a target average value 328 corresponding to the target value of the characteristic (step 809 ).
- time-series data are generated for each combination of values of p( 1 ) to p(m) included in the parameter set 321 , and an image that is multi-dimensional data is generated for each time-series data.
- the VAE 325 may be caused to learn images exhibiting states of the analysis target that changes with the passage of time.
- FIG. 9 is a flowchart illustrating an example of the searching processing performed by the data processing apparatus 301 in FIG. 3 .
- the data processing apparatus 301 inputs the initial parameters 329 to the simulator 312 (step 901 ).
- the simulator 312 generates time-series data by executing a simulation using the values of p( 1 ) to p(m) included in the initial parameters 329 and calculates a characteristic value for the time-series data (step 902 ).
- the searching unit 316 compares a difference ⁇ between the calculated characteristic value and a target value with a threshold value TH (step 903 ). If ⁇ is higher than TH (NO in step 903 ), the image generating unit 313 generates an image representing the generated time-series data (step 904 ).
- the searching unit 316 acquires average values of the latent variables Z from the generated images by using the VAE 325 (step 905 ).
- the searching unit 316 calculates change amounts of p( 1 ) to p(m) by using the average values of the latent variables Z, the regression model 326 , the coefficient of determination 327 and the target average value 328 (step 906 ) and updates the values of p( 1 ) to p(m) by using the change amounts (step 907 ).
- the data processing apparatus 301 repeats the processing in step 902 and subsequent steps by using the values of the updated p( 1 ) to p(m). If ⁇ is equal to or lower than TH (YES in step 903 ), the searching unit 316 records the current values of p( 1 ) to p(m) as proper parameters 330 , and the output unit 317 outputs the proper parameters 330 (step 908 ).
- the update process for updating the values of p( 1 ) to p(m) is repeated while the difference ⁇ between the current characteristic value and the target value is compared with the threshold value TH.
- the values of p( 1 ) to p(m) may be brought closer to the optimum value for certain. Because m values of p(i) are simultaneously updated by one update process, the proper parameters 330 may be acquired in a shorter period of time than a case where one of values of p(i) is updated.
- FIG. 10 illustrates an example of a power supply circuit of an analysis target.
- the power supply circuit in FIG. 10 includes resistors 1001 to 1019 , capacitors 1021 to 1023 , parasitic inductances 1031 to 1033 , and an inductor 1034 .
- the power supply circuit further includes a 9V-voltage source 1041 (Vi), a diode 1042 , an integrated circuit 1043 , a field-effect transistor (FET) 1044 , and an FET 1045 .
- the resistor 1019 exhibits a load resistance Rload.
- Circuit parameters representing resistance values of the resistors 1001 to 1018 are: resistor 1001 Rp 1 , resistor 1002 Rp 3 , resistor 1003 Rsim 3 , resistor 1004 Rsim 1 , resistor 1005 Rsim 2 , resistor 1006 Rg 1 , resistor 1007 Rgs 1 , resistor 1008 Rg 2 , resistor 1009 Rgs 2 , resistor 1010 Rp 2 , resistor 1011 Rp 4 , resistor 1012 Rp 5 , resistor 1013 Rp 6 , resistor 1014 Rp 7 , resistor 1015 Rl 1 , resistor 1016 Rp 10 , resistor 1017 Rp 9 , resistor 1018 Rp 11 .
- Circuit parameters representing capacitances of the capacitors 1021 to 1023 are: capacitor 1021 C 3 , capacitor 1022 C 22 , capacitor 1023 C 8
- Circuit parameters exhibiting inductances of the parasitic inductance 1031 to 1033 and the inductor 1034 are: parasitic inductance 1031 Lp 1 , parasitic inductance 1032 Lp 2 , parasitic inductance 1033 Lp 3 , inductor 1034 Lf 1
- FIG. 11 illustrates examples of images of voltage waveforms at the nodes N 1 to N 9 .
- t in Expression (5) is 1313, and the size of each of the images is 120 ⁇ 120.
- 29160 combinations corresponding to 90% of 32400 combinations are used as training data in the learning processing, and 3240 combinations corresponding to the remaining 10% are used as validation data.
- a standard configuration and learning algorithm are used in this specific example.
- the encoder 601 is a combination of a 4-step convolutional neural network (CNN) and a 2-step fully connected layer (FC), and the decoder 602 is a combination of a 1-step FC and a 2-step CNN.
- CNN convolutional neural network
- FC fully connected layer
- a cross entropy error between the input image X and the output image X′ is used.
- the configurations of the data processing apparatus 101 in FIG. 1 and the data processing apparatus 301 in FIG. 3 are merely examples, and some components may be omitted or changed according to the use or conditions of the data processing apparatuses.
- the learning unit 314 and the regression analysis unit 315 may be omitted in the data processing apparatus 301 in FIG. 3 .
- the simulator 312 may be omitted.
- the output unit 317 may be omitted.
- FIGS. 2 , 8 , and 9 are merely an example and may have some portions of the processing omitted or modified in accordance with the configuration or the conditions of the data processing apparatus.
- the learning processing in FIG. 8 may be omitted.
- the processing in step 802 in FIG. 8 and step 902 in FIG. 9 may be omitted.
- the VAE 325 illustrated in FIGS. 4 and 6 is merely an example, and the configurations of the encoders and the decoders may be changed according to the use or conditions of the data processing apparatus.
- the compression model 121 that compresses the dimensions of data may be any other model than the VAE 325 .
- the latent space illustrated in FIG. 5 is merely an example, and the dimensions of the latent space change according to the analysis target.
- the function F(x) illustrated in FIGS. 7 A and 7 B is merely an example, and any other monotonically increasing function may be used as the function F(x).
- the learning processing illustrated in FIGS. 10 to 12 is merely an example, and the analysis target is changed according to the use of the data processing apparatus.
- Expressions (1) to (26) are merely an example, and the data processing apparatus may perform the learning processing and the searching processing by using other expressions.
- the coefficient of determination Ri 2 in Expression (17) another index indicating the reliability of the regression model 326 may be used to calculate ⁇ p(i) of Expression (21).
- the ramp function in Expression (24) and the sigmoid function in Expression (25) any other monotonically increasing function may be used as the function F(x).
- FIG. 13 illustrates a configuration example of an information processing apparatus used as the data processing apparatus 101 in FIG. 1 and the data processing apparatus 301 in FIG. 3 .
- the information processing apparatus in FIG. 13 includes a central processing unit (CPU) 1301 , a memory 1302 , an input device 1303 , an output device 1304 , an auxiliary storage device 1305 , a medium driving device 1306 , and a network coupling device 1307 . These components are coupled to each other by a bus 1308 .
- CPU central processing unit
- the memory 1302 is a semiconductor memory such as a read-only memory (ROM), a random-access memory (RAM), a flash memory, and stores programs and data used for processing, for example.
- the memory 1302 may be used as the storage unit 111 in FIG. 1 or the storage unit 311 in FIG. 3 .
- the CPU 1301 (processor) operates as the changing unit 112 in FIG. 1 by executing a program by using the memory 1302 , for example.
- the CPU 1301 also operates as the simulator 312 , the image generating unit 313 , the learning unit 314 , the regression analysis unit 315 and the searching unit 316 in FIG. 3 by executing the program by using the memory 1302 .
- the input device 1303 is a keyboard, a pointing device, or the like, and is used for inputting instructions or information from an operator or a user, for example.
- the output device 1304 is a display device, a printer, a speaker or the like, for example, and is used for outputting inquiries or instructions and a processing result to the operator or the user.
- the processing result may be the proper parameters 330 or may be a circuit diagram, a design drawing, an analysis result or the like.
- the output device 1304 may be used as the output unit 317 in FIG. 3 .
- the auxiliary storage devices 1305 is a magnetic disk device, an optical disk device, a magneto-optical disk device, a tape device, or the like, for example.
- the auxiliary storage device 1305 may be a hard disk drive or a flash memory.
- the information processing apparatus may cause the auxiliary storage device 1385 to store programs and data and load the programs and data into the memory 1302 for use.
- the auxiliary storage device 1305 may be used as the storage unit 111 in FIG. 1 or the storage unit 311 in FIG. 3 .
- the medium driving device 1306 drives the portable recording medium 1309 and accesses the recorded contents.
- the portable recording medium 1309 is a memory device, a flexible disk, an optical disk, a magneto-optical disk, or the like.
- the portable recording medium 1309 may be a compact disk read-only memory (CD-ROM), a digital versatile disk (DVD), a Universal Serial Bus (USB) memory, or the like.
- An operator or a user may cause the portable recording medium 1309 to store programs and data and load the programs and data into the memory 1302 for use.
- the computer readable recording medium that stores programs and data used for processing is a physical (non-transitory) recording medium, such as the memory 1302 , the auxiliary storage device 1305 , or the portable recording medium 1309 .
- the network coupling device 1307 is a communication interface circuit which is coupled to a communication network such as a local area network (LAN) and a wide area network (WAN), and performs data conversion for communication.
- the information processing apparatus may receive programs and data from an external device through the network coupling device 1307 and load the programs and data into the memory 1302 for use.
- the network coupling device 1307 may be used as the output unit 317 in FIG. 3 .
- the information processing apparatus may not include all the components in FIG. 13 , and it is also possible to omit some components according to the use or condition. For example, when an interface with the user or the operator is not required, the input device 1303 and the output device 1304 may be omitted. In a case where the portable recording medium 1309 or the communication network is not used, the medium driving device 1306 or the network coupling device 1307 may be omitted.
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Abstract
Description
Π={P1,P2, . . . ,Pk} (1)
Pj=(pj(1),pj(2), . . . ,pj(m)) (2)
┌={ω1,ω2, . . . ,ωk} (3)
ωj=(V1,V2, . . . ,Vo) (4)
Va=(va(1),va(2), . . . ,va(t)) (5)
∧={η1,η2, . . . ,ηk} (6)
ξ={X1,X2, . . . ,Xk} (7)
Xj=(G2,G2, . . . ,Go) (8)
Ga=(ra(1),ra(2), . . . ,ra(u)) (9)
Z=μ+Σ 1/2⊙ε=(z1,z2, . . . ,zn) (10)
L=D KL(Q(Z|X)∥N(0,I))−E[log R(X|Z)] (11)
M={μ1,μ2, . . . ,μk} (12)
μj=(μj(1),μj(2), . . . ,μj(n)) (13)
yi(z1,z2, . . . ,zn)=αi+βi(1)z1+βi(2)z2+ . . . +βi(n)zn (15)
yj(i)=αi+βi(1)μj(1)+βi(2)μj(2)+ . . . +βi(n)μj(n) (16)
Δp(i)=F(Ri 2)Δyi (21)
Δyi=yi(μt)−yi(μc) (22)
p(i)=p(i)+Δp(i) (23)
k=36×100×9=32400 (26)
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